Design: Blocked RCT, with 2 levels, and randomization done at level 1 (individual level).

Models: Constant treatment effects, fixed treatment effects, and random treatment effects.

Power Validation

Default parameters:

  • M = 3
  • J = 20
  • rho: \(\rho\) = 0.5
  • ATE ES = 0.125, 0.125, 0.125
  • R2.1: \(R^2_1\) = 0.1, 0.1, 0.1

Parameters by model type:

  • Omega: \(\omega_2 = 0\) for constant effects, \(\omega_2\) = 0.1 for fixed and random
  • ICC: \(\text{ICC}_2 = 0\) for constant and fixed effects, \(\text{ICC}_2\) = 0.2, 0.2, 0.2 for random effects

Assumptions:

  • Two-level design: \(\text{ICC}_3 = 0\), \(\omega_3 = 0\), \(K = 1\)

Varying school size

\(\bar{n}\) = 100

\(\bar{n}\) = 75

\(\bar{n}\) = 50

Varying R2

\(R^2_1 =\) 0.6, 0.6, 0.6

\(R^2_2 =\) 0.6, 0.6, 0.6 (This should not affect power!)

\(R^2_1 =\) 0, 0, 0 \(R^2_2 =\) 0, 0, 0

Varying rho

\(\rho =\) 0.2

\(\rho =\) 0.8

Varying true positives

ATE (ES) = 0.125, 0, 0

Varying ICC

\(\text{ICC}_2\) = 0.8, 0.8, 0.8

MDES validation

Sample size validation